Question: Solve for $x$ and $y$ using substitution. ${-2x-2y = 6}$ ${y = 3x-7}$
Since $y$ has already been solved for, substitute $3x-7$ for $y$ in the first equation. ${-2x - 2}{(3x-7)}{= 6}$ Simplify and solve for $x$ $-2x-6x + 14 = 6$ $-8x+14 = 6$ $-8x+14{-14} = 6{-14}$ $-8x = -8$ $\dfrac{-8x}{{-8}} = \dfrac{-8}{{-8}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = 3x-7}\thinspace$ to find $y$ ${y = 3}{(1)}{ - 7}$ $y = 3 - 7$ $y = -4$ You can also plug ${x = 1}$ into $\thinspace {-2x-2y = 6}\thinspace$ and get the same answer for $y$ : ${-2}{(1)}{ - 2y = 6}$ ${y = -4}$